{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f8ba3161",
   "metadata": {},
   "source": [
    "# Interpretability 8: Adding auxiliary variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6535c1f2",
   "metadata": {},
   "source": [
    "When we do a regression task, it might be good to include auxiliary input variables, even though they might be dependent on other variables. For example, to regress $m(m_0, v, c)=m_0/\\sqrt{1-(v/c)^2}$, it is desirable to include the dimensionaless varabile $\\beta = v/c$ as a separate input variable. If we also know this is a task in relativity, we may also include $\\gamma=1/\\sqrt{1-(v/c)^2}$ because $\\gamma$ appears frequently in relativity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3b818211",
   "metadata": {},
   "outputs": [],
   "source": [
    "from kan.MultKAN import MultKAN\n",
    "from sympy import *\n",
    "from kan.utils import create_dataset, augment_input\n",
    "import torch\n",
    "\n",
    "seed = 1\n",
    "torch.manual_seed(seed)\n",
    "torch.set_default_dtype(torch.float64)\n",
    "\n",
    "input_variables = m0, v, c = symbols('m0 v c')\n",
    "\n",
    "# define auxillary variables\n",
    "beta = v/c\n",
    "gamma = 1/sqrt(1-beta**2)\n",
    "\n",
    "aux_vars = (beta, gamma)\n",
    "\n",
    "f = lambda x: x[:,[0]]/torch.sqrt(1-x[:,[1]]**2/x[:,[2]]**2)\n",
    "dataset = create_dataset(f, n_var=3, ranges=[[0,1],[0,0.9],[1.1,2]])\n",
    "\n",
    "# add auxillary variables\n",
    "dataset = augment_input(input_variables, aux_vars, dataset)\n",
    "input_variables = aux_vars + input_variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c386c245",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    }
   ],
   "source": [
    "model = MultKAN(width=[5,[0,1]], mult_arity=2, grid=3, k=3, seed=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "59c8b0d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 14 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model(dataset['train_input'])\n",
    "model.plot(in_vars=input_variables, out_vars=[m0/sqrt(1-v**2/c**2)], scale=1.0, varscale=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2951afef",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 5.13e-04 | test_loss: 6.64e-04 | reg: 3.18e+00 | : 100%|█| 50/50 [00:07<00:00,  7.10it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, steps=50, lamb=1e-5, lamb_coef=1.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "71656f49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 14 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(in_vars=input_variables, out_vars=[m0/sqrt(1-v**2/c**2)], scale=1.0, varscale=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b2b17686",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.2\n"
     ]
    }
   ],
   "source": [
    "model = model.prune(edge_th=5e-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bdd1a705",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 14 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(in_vars=input_variables, out_vars=[m0/sqrt(1-v**2/c**2)], scale=1.0, varscale=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d2e07789",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 3.15e-06 | test_loss: 1.99e-05 | reg: 2.74e+00 | : 100%|█| 100/100 [00:10<00:00,  9.48"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, steps=100, lamb=0e-3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6e8cfa58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fixing (0,0,0) with 0\n",
      "fixing (0,0,1) with 0\n",
      "fixing (0,1,0) with x, r2=0.999998976626967, c=1\n",
      "fixing (0,1,1) with 0\n",
      "fixing (0,2,0) with 0\n",
      "fixing (0,2,1) with x, r2=0.9999999998075859, c=1\n",
      "fixing (0,3,0) with 0\n",
      "fixing (0,3,1) with 0\n",
      "fixing (0,4,0) with 0\n",
      "fixing (0,4,1) with 0\n",
      "saving model version 0.4\n"
     ]
    }
   ],
   "source": [
    "model.auto_symbolic()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a230671a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.0 \\cdot \\left(0.000189505852432992 - \\frac{0.817980335069318}{\\sqrt{1 - \\frac{v^{2}}{c^{2}}}}\\right) \\left(- 1.22278885546569 m_{0} - 2.33019836537451 \\cdot 10^{-7}\\right)$"
      ],
      "text/plain": [
       "1.0*(0.000189505852432992 - 0.817980335069318/sqrt(1 - v**2/c**2))*(-1.22278885546569*m0 - 2.33019836537451e-7)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sf = model.symbolic_formula(var=input_variables)[0][0]\n",
    "sf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c8414225",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{m_{0}}{\\sqrt{1 - \\frac{v^{2}}{c^{2}}}}$"
      ],
      "text/plain": [
       "m0/sqrt(1 - v**2/c**2)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan.utils import ex_round\n",
    "\n",
    "nsimplify(ex_round(ex_round(ex_round(sf,6),3),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "151a6d23-a38f-439f-b9ec-30622f8b045c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
